Should I write potential PhD advisors outside of the application process?

Faculty vary widely in whether they pay attention to these emails. While it generally won’t hurt you, it can be difficult to break through the noise of a professor’s inbox. 

Your message is more likely to stand out if you can explain why you would be a good match for the professor’s research group. The more specific you can be, the better. 

If you have not yet submitted your application,  consider if there is a place for this information in your application, where somebody is sure to read it.